where the tensors \(G_k \in \mathbb {R}^{r_{k-1}\times n_k\times r_k}\)  are called TT-cores. Khrulkov et al. [1]} introduce bilinear units to represent TT-cores. Given \(x\in \mathbb {R}^m, y\in \mathbb {R}^n\)  and \(G\in \mathbb {R}^{m\times n\times k}\) , a bilinear unit performs a map \(G: \mathbb {R}^m \times \mathbb {R}^n \rightarrow \mathbb {R}^k\) , written as \(G(x,y) = z\) . Based on the bilinear units, they show that a recurrent neural network realizes the TT-decomposition of the weight tensor (Figure REF ).
Similarly, Khrulkov et al. [1]} show that the Canonical (CP) decomposition [3]}, with the form of
\(\nonumber \mathcal {X}^{i_1i_2\ldots i_d} = \sum _{\alpha = 1}^{r} v_{1,\alpha }^{i_1} v_{2, \alpha }^{i_2} \ldots v_{d,\alpha }^{i_d},\) 
